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A Numerical Study of the 6 May 2012 Tsukuba City Supercell Tornado. Part I: Vorticity Sources of Low-Level and Midlevel Mesocyclones

WATARU MASHIKO Meteorological Research Institute, Tsukuba, Japan

(Manuscript received 29 March 2015, in ﬁnal form 6 December 2015)

ABSTRACT

On 6 May 2012, an F3 supercell tornado, one of the most destructive tornadoes ever recorded in Japan, hit Tsukuba City in eastern Japan and caused severe damage. To clarify the generation mechanisms of the tornadic storm and tornado, high-resolution numerical simulations were conducted under realistic environmental conditions using triply nested grids. The innermost simulation with a 50-m mesh successfully reproduced the Tsukuba City tornadic supercell storm. In this study (the first of a two-part study), the vorticity sources responsible for mesocyclogenesis prior to tornadogenesis were investigated by analyzing vortex lines and the evolution of circulation of the mesocyclones. Vortex lines that passed through the midlevel mesocyclone (4-km height) originated from the environmental streamwise vorticity, whereas the low-level mesocyclone and low-level mesoanticyclone were connected by several arching vortex lines over the rear-flank downdraft associated with the hook-shaped distribution of hydrometeors (hereafter hook echo). Most of the circulation for the circuit surrounding the midlevel mesocyclone was conserved, although the baroclinity associated with positive buoyancy within the storm led to an up-and-down trend. The circulation of the material circuit encircling the low-level mesocyclone showed a gradual increase caused by baroclinity along the forward-flank gust front. Friction also had a positive net effect on the circulation. In contrast, most of the negative circulation of the low-level mesoanticyclone was rapidly acquired owing to baroclinity around the tip of the hook echo. Just after tornadogenesis, the low-level mesocyclone intensified significantly and developed upward, which caused retrograde motion of the midlevel mesocyclone.

1. Introduction sometimes observed on the anticyclonic shear side of the rear-flank downdraft (RFD) outflow as a counterpart Our understanding of the structure, evolution, and of the low-level mesocyclone (e.g., Brandes 1981; dynamics of supercell storms has been greatly advanced Markowski et al. 2008, 2012a; Atkins et al. 2012). Sev- by observational, numerical, and theoretical studies eral observational and numerical studies have shown conducted over the past few decades. As many previous that supercell tornadogenesis is preceded by the in- studies (e.g., Browning 1964; Lemon and Doswell 1979; tensification of the low-level mesocyclone (Rasmussen Klemp 1987) have indicated, supercells are character- et al. 2000; Mashiko et al. 2009; Schumacher and ized by the existence of a persistent mesocyclone with a Boustead 2011; Schenkman et al. 2014) because the strong updraft within a convective storm. In the early dynamically induced pressure deficit associated with the stage of supercell storms, a strong rotating updraft forms low-level mesocyclone intensifies the updraft near at midlevel (;4-km height, hereafter referred to as a the surface (e.g., Wicker and Wilhelmson 1995; Noda midlevel mesocyclone). As the storm develops, a low- and Niino 2010). Although numerous observational level mesocyclone (;1-km height) becomes prominent, studies (e.g., Wakimoto and Cai 2000; Markowski et al. and a low-level mesoanticyclone (;1-km height) is 2002, 2011; Wakimoto et al. 2004) have reported that nontornadic supercell storms are often similar in structure and evolution to tornadic supercells, Trapp et al. Corresponding author address: Wataru Mashiko, Meteorological Research Institute, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, (2005) showed statistically that more than 40% of low- Japan. level mesocyclones detected by a Doppler radar net- E-mail: [email protected] work in the United States are associated with tornadoes.

DOI: 10.1175/MWR-D-15-0123.1

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Thus, an understanding of the formation mechanisms of vorticity. Numerical studies of supercell storms con- mesocyclones not only increases scientific knowledge ducted during the 1990s or earlier (e.g., Klemp and but also is crucial for improving operational tornado Rotunno 1983; Wicker and Wilhelmson 1995) also sug- warning systems. Nevertheless, the formation mecha- gested that the baroclinity along the forward-flank gust nisms of low-level mesocyclones remain unclear, and front (FFGF) might be a dominant vorticity source re- one of the most fundamental uncertainties pertains to sponsible for the development of low-level mesocy- the vorticity sources responsible for mesocyclogenesis in clones. Wicker (1996) indicated that the interaction supercell storms at low levels. between the environmental horizontal vorticity near the The vorticity source of midlevel mesocyclones in surface and the baroclinically generated horizontal supercell storms is relatively well understood. Using vorticity along gust fronts is crucial for the development vortex line analyses, numerous previous studies (Davies- of a low-level mesocyclone. Rotunno and Klemp (1985) Jones 1984; Rotunno and Klemp 1985; Markowski et al. analyzed the circulation of a material circuit surrounding a 2008, 2012a) revealed that midlevel mesocyclones ac- low-level vortex and estimated the baroclinic contribu- quire vertical vorticity aloft by the tilting of horizontal tion directly. They found that the circulation originated vorticity associated with environmental vertical wind mostly from baroclinity along the gust fronts. However, shear. Indeed, storm-relative environmental helicity the finding of strong baroclinity along gust fronts (SREH) (e.g., Davies-Jones et al. 1990), which is calcu- within a storm in the aforementioned simulation results lated by integrating vertically the scalar product of the is disputable, because the cold pools simulated behind environmental horizontal vorticity and storm-relative the gust fronts were excessively strong compared to wind vectors, is frequently used as an index of the po- those reported by observation (e.g., Davies-Jones 2006; tential for supercell genesis. Although the possible im- Shabbott and Markowski 2006). portance of the baroclinic effect on a midlevel rotation More recent idealized numerical studies have in- was also acknowledged (Davies-Jones et al. 2001), the dicated that the RFD and/or the FFD plays a dominant contribution of the environmental vertical wind shear to role in creating vertical vorticity and bringing it to the the vorticity source of a midlevel mesocyclone has thus ground (Dahl et al. 2014; Markowski and Richardson far not been quantified by analyzing the circulation of the 2014; Parker and Dahl 2015). The baroclinically gener- material circuit tracked backward from the midlevel ated horizontal vorticity is tilted upward during the mesocyclone. parcel descent. Markowski and Richardson (2014) also Numerous studies of low-level mesocyclones have analyzed the vorticity forcing along a trajectory initiated focused on the RFD as the vorticity source. Vortex lines from a region of negative vertical vorticity associated passing through low-level mesocyclones form arches with a near-surface anticyclonic vortex. The vorticity over the RFD region, which suggests that the vorticity is vector generated by baroclinity is inclined below the baroclinically generated by horizontal buoyancy gradi- descending parcel trajectory. These results are consis- ents in the RFD region (Straka et al. 2007; Markowski tent with previous studies showing arching vortex lines et al. 2008, 2012a). If the leading edge of the vortex rings over the RFD region (Straka et al. 2007; Markowski produced by baroclinity associated with the RFD region et al. 2008, 2012a). is lifted by updrafts due to the gust front or the low-level However, these idealized numerical studies of the mesocyclone, arching vortex lines form and connect the low-level mesocyclones and mesoanticyclones did not cyclonic and anticyclonic vortices. These storm- evaluate the frictional effect despite their consideration generated vortex lines and the environmental vorticity of near-surface phenomena; the circulation of material usually have different orientations (e.g., Markowski circuits was changed solely by baroclinity and turbulent et al. 2008). mixing while neglecting surface friction. Using Doppler radar data, Markowski et al. (2012b) In this study, which is the first part of a two-part quantitatively evaluated the vorticity sources of a low- study, high-resolution simulation results were used to level mesocyclone in a supercell by analyzing the cir- investigate a tornadic supercell that caused severe culation of the material circuit surrounding the vertical damage to Tsukuba City, Japan, on 6 May 2012. A vorticity maximum associated with the low-level meso- simulation with a 50-m horizontal grid spacing was cyclone. They revealed that the baroclinity associated conducted under realistic environmental conditions that with the forward-flank downdraft (FFD) in the pre- included the surface drag. The aim of the study is to cipitation region is the primary source of circulation, and quantify the vorticity sources of the low-level and mid- that the RFD associated with the descending reflectivity level mesocyclones and the low-level mesoanticyclone core (e.g., Byko et al. 2009) modulates the low-level in the supercell. In addition to analyzing the configura- rotation and buoyancy field instead of generating tion of three-dimensional vortex lines, the evolution of

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FIG. 1. (a) Topographic map of eastern Japan showing the calculation domains of NHM1km (entire map), NHM250m (within the solid rectangle), and NHM50m (within the dashed rectangle) (see section 3). (b) Enlarged view of the NHM50m domain, which includes the area around Tsukuba City, showing the tracks of the simulated and observed tornadoes. circulation about the material circuits surrounding the 37 injuries along with severe property damage, with 76 mesocyclones was examined to directly assess the con- houses completely destroyed (Japan Meteorological tributions of baroclinity and frictional drag to meso- Agency 2012). The tornado was generated at about 1235 cyclogenesis. The baroclinic field around the midlevel Japan standard time (JST; JST 5 UTC 1 9 h) near mesocyclone was also investigated. In Mashiko (2016, Tsukuba City, and it moved east-northeastward at about 2 manuscript submitted to Mon. Wea. Rev., hereafter Part 60 km h 1 across Tsukuba City before eventually dissi- II) the generation mechanisms of the simulated tornado pating at about 1255 JST, when it encountered a in the Tsukuba supercell were investigated. mountainous area (Fig. 1b). The damage path was about The remainder of this paper is structured as follows: 17 km long. Section 2 presents a brief overview of the 6 May 2012 The tornadic storm developed at the southern tip of a Tsukuba City tornadic supercell. Section 3 describes north–south-oriented rainband that was accompanied the experimental design of the numerical simulations. by wind shear near the surface. The storm had the typ- The simulated environmental fields around the storm ical characteristics of a supercell. A hook-shaped echo are presented in section 4. Section 5 presents an pattern (Fig. 2a) and a strong cyclonic rotation associ- overview of the evolution of the simulated storm, in- ated with a mesocyclone were detected by a C-band cluding tornadogenesis. In section 6, mesocyclogenesis Doppler radar about 15 km from the storm (Yamauchi of the midlevel mesocyclone, the low-level mesocy- et al. 2013). The storm also had a ‘‘vault’’ structure in the clone, and the low-level anticyclonic vortex is de- radar reflectivity field, and the height of the echo top scribed on the basis of analyses of vortex lines and exceeded 10 km (not shown). However, the horizontal circulation. Section 7 describes the structure changes dimensions of the Tsukuba storm were slightly smaller of the storm before and just after tornadogenesis. Fi- than those of a typical supercell in the midwestern nally, in section 8, the results are summarized and United States (e.g., Markowski 2002). Using polari- conclusions are presented. metric radar observations, Yamauchi et al. (2013) performed a detailed dynamical analysis of the supercell storm as well as the tornado itself. 2. Case overview Figure 3 shows the surface synoptic weather map at On 6 May 2012, an F3 tornado, one of the most de- 0900 JST. A low pressure system was situated over the structive tornadoes ever recorded in Japan, hit Tsukuba Japan Sea, and low-level southerly winds with warm and City in eastern Japan (Fig. 1) and caused one fatality and moist air prevailed in eastern Japan. Shoji et al. (2014)

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FIG. 2. (a) Reﬂectivity (dBZ) observed at 1239 JST by the lowest elevation PPI scan (elevation angle 0.58) of the C-band radar situated about 15 km from the storm (courtesy of Hiroshi Yamauchi). The red circle at the tip of the hook echo shows the location of the observed tornado. (b) Mixing ratio of hydrometeors (sum of rain, snow, and hail/graupel) at a height of 1 km at 1214 JST simulated by NHM50m. Arrows indicate storm-relative winds. (c) Close-up of the simulated vertical vorticity at z* 5 10 m within the red dashed rectangular area in (b). Arrows indicate ground-relative winds. The contour lines show sea level pressure and are drawn at 2-hPa intervals.

estimated the precipitable water vapor around the previous studies (e.g., Schenkman et al. 2014). Subgrid Tsukuba storm based on observations of ground-based turbulent mixing is treated using a 1.5-order turbulent stations of the global navigation satellite system and kinetic energy closure scheme (Deardorff 1980). Surface reported that high precipitable water vapor (more than fluxes are computed by the bulk method formulated by 40 mm) was present in the inflow region of the storm. Beljaars and Holtslag (1991). Topography and vegeta- Moreover, an upper-level trough accompanied by cold tion datasets with a 50-m mesh provided by the Geo- air was approaching eastern Japan and created a fa- spatial Information Authority of Japan were used for vorable condition for tornadic supercell genesis, com- the simulations. The terrain-following vertical co- bining strong static instability and vertical wind shear ordinate of z* is adopted: z* 5 H(z 2 zs)/(H 2 zs), with veering (as discussed in section 4). In fact, the where zs and H are the surface and model-top heights, north–south-oriented rainband contained at least two respectively.1 other tornadic storms to the north of Tsukuba City To explicitly resolve the tornado, which had a scale (Japan Meteorological Agency 2012). of a few hundred meters, a high-resolution simulation with a horizontal grid spacing of 50 m (hereafter referred to as NHM50m) was performed by using triply 3. Experimental design and brief verification nested one-way grids. Horizontal grid spacings of 1 km Numerical simulations of the Tsukuba supercell tor- and 250 m were adopted for the outermost model nado were conducted using the Japan Meteorological (NHM1km) and intermediate model (NHM250m), re- Agency Nonhydrostatic Model (JMANHM; Saito et al. spectively. The model domains are shown in Fig. 1; the 2006), which is an operational model of the Japan NHM50m domain (1300 3 1100 horizontal grid points) Meteorological Agency (JMA). The JMANHM has includes the actual tornado path within a 65 km 3 55 km performed well in simulating various mesoscale phe- area around Tsukuba City. The model designs are nomena, including supercell tornadogenesis (Mashiko summarized in Table 1. The innermost model, et al. 2009). The model includes a bulk-type cloud mi- NHM50m, included 100 vertical levels with variable grid crophysics scheme (Ikawa et al. 1991; Murakami 1990) interval, which increased from 20 m at the surface to based on the formulation of Lin et al. (1983), and it predicts the mixing ratios of six water species (water vapor, cloud water, rain, cloud ice, snow, and hail/ 1 This paper focuses on the Tsukuba supercell tornadogenesis, graupel) and the number concentrations of ice-phase which occurred on a nearly flat plain about 20 m above sea level particles (cloud ice, snow, and hail/graupel). The rain (Fig. 1b). Thus, z* is almost equivalent to the height above 2 intercept parameter is set to 8 3 106 m 4, as in most ground level.

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500 m 3 500 m area. The storm motion was defined as the averaged movement of the low-level mesocyclone from 1203 to 1213 JST. The simulated supercell exhibited a hook-shaped hydrometeor pattern (hereafter referred to as hook echo), and cyclonic rotation associated with a low-level mesocyclone was evident in the storm-relative wind field (Fig. 2b). The simulated tornado, which had large vertical vorticity of more than 2 1.0 s 1 and a pressure deficit of about 20 hPa near the surface, was located at the tip of the simulated hook echo. Figure 4 shows time series of the vertical vorticity and horizontal wind velocity maxima at z* 5 10 m and of sea level pressure minimum within a radius of 2.5 km from the center of the low-level mesocyclone. Rapid increases of vertical vorticity and wind velocity together with the abrupt decrease of pressure occurred at around 1208 JST, which can be defined as the timing of tornado- 2 genesis. The vertical vorticity reached 0.78 s 1 at 1208:20 JST, and it was accompanied by an increase in the wind 21 FIG. 3. Surface synoptic weather map at 0900 JST 6 May 2012. velocity of more than 20 m s in less than a minute. The Contours indicate isobars at sea level (hPa). simulated tornado significantly intensified around 1214 JST, and at its peak the vertical vorticity and wind ve- 2 2 260 m at the model top (H 5 15 640 m). The lowest level locity were 1.63 s 1 and 67.2 m s 1, respectively. Then was at z* 5 10 m. around 1218 JST, the simulated tornado encountered a To obtain the realistic environmental conditions mountainous area and suddenly weakened and dissi- around the storm, the JMA mesoscale analysis data pated, similar to the observed Tsukuba Tornado with a horizontal grid spacing of 5 km, which are oper- (Fig. 1b). The simulated track was close to the observed ationally produced by a four-dimensional variational track (Fig. 1b). data assimilation technique based on JMANHM (Japan Meteorological Agency 2013), were used for the initial 4. Environment around the supercell storm and boundary conditions of NHM1km. The NHM1km simulation was initialized at 0900 JST 6 May, more than A wind hodograph from 0- to 6-km altitude at a point 3 h before tornadogenesis. The NHM50m simulation 20 km south of the storm 10 min prior to tornadogenesis started at 1150 JST and was integrated for 30 min. The is shown in Fig. 5a. The environmental wind field was initial and lateral boundary data for NHM50m were characterized by strong vertical shear with veering at obtained from the simulation results of NHM250m. low levels; the winds were southerly below 500 m and NHM50m successfully simulated both the Tsukuba south-southwesterly to southwesterly above that eleva- supercell storm and the tornado, except that the simu- tion. The orientation of the near-ground shear is con- lated tornado formed about 25 min earlier than the ob- sistent with surface friction. The southerly wind of about 2 served tornado (Fig. 2). In this study, the low-level 4ms 1 at the lowest model level nearly matched the mesocyclone center was defined as the point of maxi- surface observation at Tsukuba City. The motion of the mum vertical vorticity at 1-km height averaged over a low-level mesocyclone at a height of 1 km (Fig. 5a) was

TABLE 1. Design of the model experiments.

NHM1km NHM250m NHM50m Dimensions (x, y, z) 1000 3 1000 3 62 1200 3 1100 3 70 1300 3 1100 3 100 Horizontal grid spacing (m) 1000 250 50 Model top H (m) 19 805 18 432 15 640 Vertical grid spacing Dz* (m) 40–640 40–516 20–260 Large time step (s) 5 2 0.4 Integration time (JST) 0900–1300 1100–1300 1150–1220

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FIG. 4. Time series of vertical vorticity (blue line) and horizontal wind velocity (green line) maxima at z* 5 10 m and minimum sea level pressure (red line) within a radius of 2.5 km from the low-level mesocyclone center. The low-level mesocyclone center was deﬁned as the point of maximum vertical vorticity at 1-km height averaged over a 500-m2 area.

68% of the magnitude of the 0–6-km average wind and for a typical supercell storm such as occurs in the mid- deviated by 248 to the right relative to the averaged wind western United States. direction. This deviation is a typical characteristic of supercell storms, and it is caused by an upward dynamic 5. Evolution of the supercell tornado pressure gradient force on the right flank of an updraft in the environmental veering shear (Rotunno and Klemp Figures 6a–c show the time–height diagrams of verti- 2 1982). The 0–3-km SREH value was 554 m2 s 2, which is cal vorticity maxima, pressure perturbation minima comparable to or a little smaller than that of a tornadic from the initial averaged state at 1150 JST, and updraft supercell occurring in a tropical cyclone environment maxima around the low-level mesocyclone from 1155 to (Molinari and Vollaro 2008; Mashiko et al. 2009), but 1220 JST, which provide an overview of the evolution larger than that in a typical continental supercell envi- of a tornadic storm. Throughout the period, a pressure ronment (e.g., Thompson et al. 2003, 2007). deficit associated with a midlevel mesocyclone was evi- Vertical profiles of the simulated thermodynamic dent around a height of 4 km. From 1204 JST (4 min fields are shown in Fig. 5b. The low-level air below prior to tornadogenesis), the vertical vorticity and up- 940 hPa was warm and highly humid, whereas the tem- drafts started to intensify, particularly below 1 km, in- perature was relatively low around 400 hPa under the dicating the development of a low-level mesocyclone. influence of the upper-level trough, leading to the un- Rapid intensification of vertical vorticity and a sudden stable atmospheric condition. The maximum unstable pressure drop occurred at a height of around 1 km just convective available potential energy (MUCAPE) was before tornadogenesis, resulting in strong updrafts ex- 2 2 2040 J kg 1 for an air parcel at z* 5 298 m, which is ceeding 20 m s 1 even at 500-m height. After that, the within the range of typical supercell environments (e.g., vertical vorticity intensified near the surface, and the McCaul and Weisman 1996; Thompson et al. 2003) tornado was subsequently generated at 1208 JST. After and much larger than that of tropical cyclone environ- the intensification of the low-level mesocyclone, its as- ments (e.g., McCaul 1991; Mashiko et al. 2009; Molinari sociated strong vertical vorticity and significant pressure and Vollaro 2010). In addition, the atmosphere was drop appeared to develop upward toward midlevels with unsaturated throughout the troposphere and a dry time, indicating that the low-level mesocyclone contin- layer existed around 700–900 hPa, in contrast to the ued to develop and formed a deep structure. This typhoon-associated supercell case (Mashiko et al. 2009). structure change is discussed in more detail in section 7. The Tsukuba tornadic supercell formed in an environ- Horizontal distributions of the supercell structures ment with large convective available potential energy until just after tornadogenesis are shown in Figs. 7 and 8. (CAPE) and SREH, which provided favorable conditions The hydrometeor distribution became deformed into a

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low-level cyclonic circulation with a large positive vertical vorticity and the anticyclonic circulation with a large negative vertical vorticity significantly intensified about 2 min prior to tornadogenesis (Fig. 8e). However, the low-level mesoanticyclone weakened just before tornadogenesis (cf. Figs. 8e and 8f). The FFGF and rear-flank gust front (RFGF) were directed from north-northeast to south-southwest and separated environmental southerly winds from the storm-generated westerly winds (Figs. 7a–c and 8g–i). The RFGF curved gradually to the southwest by the effect of the strong westerly outflow near the storm center. The FFGF might correspond to the ‘‘left-flank convergence boundary’’ described by Beck and Weiss (2013) because its orientation and location differed from those of a traditional FFGF as analyzed by Lemon and Doswell (1979). The cold pools behind the gust fronts had a 2–3-K deficit in potential temperature. As has been shown in previous studies (e.g., Lemon and Doswell 1979), the tornado was generated on the RFGF close to its intersection with the FFGF, which was almost directly beneath the low-level mesocyclone (Figs. 8f and 8i). The simulated storm shares obvious features with a typical ‘‘classic’’ tornadic supercell (e.g., Noda and Niino 2010; Markowski et al. 2012a). The generation process of the simulated tornado is investigated in further detail in Part II. At midlevel (;4-km height), a broad mesocyclone with a pressure deficit of more than 4 hPa and large vertical vorticity was present 5 min prior to tornadogenesis (Fig. 8a). This midlevel mesocyclone was located about 3 km ahead (on the east-northeast side) of the low-level mesocyclone until 2 min prior to tornadogenesis (Figs. 8b,e), but it slowly moved and was nearly directly above the low-level mesocyclone by the time of tornadogenesis (Figs. 8c,f). FIG. 5. (a) Hodograph simulated by NHM50m at a point 20 km south of the low-level mesocyclone at 1158 JST (10 min prior to Hereafter, this paper focuses on the vorticity sources of tornadogenesis), calculated from the averaged winds over a 1-km2 the midlevel mesocyclone (4-km height) 5 min prior to area. Numerals next to the black circles denote height (km). The tornadogenesis (Fig. 8a) and just after tornadogenesis solid arrow shows the low-level mesocyclone motion, and the dashed (Fig. 8c), of the low-level mesocyclone (1-km height) 2 min arrow indicates 75% of the magnitude of the mass-weighted average prior to tornadogenesis (Fig. 8e), and of the low-level wind from the surface to a height of 6 km. (b) Emagram at the same location and time as (a) showing temperature (solid red line) and mesoanticyclone (1-km height) 2 min prior to tornado- dewpoint (dashed blue line). genesis (Fig. 8e). In Part II, the vorticity sources and generation mechanisms of the incipient vortex (Fig. 8h) and of distinct hook echo as the cyclonic rotation, along with the tornado just after its genesis (Fig. 8i) are investigated. the strong updraft, intensified with time. The low-level mesocyclone was located inside the hook, and a low- 6. Analyses of vortex lines and circulations level anticyclonic circulation was present to the south- a. Analysis techniques west of the low-level mesocyclone (Figs. 7d–f). A strong RFD outflow region with northwesterly winds was Vortex line analysis was performed to elucidate the nearly coincident with the hook echo pattern. The tip of vorticity sources and dynamics of each mesocyclone. A the hook echo and the associated RFD region were lo- second-order Runge–Kutta scheme was used to calculate cated between the counter-rotating vortices. Both the the vortex lines. They were computed above z* 5 10 m

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FIG. 6. Time–height diagrams of (a) maximum vertical vorticity, (b) minimum pressure perturbation from the horizontally averaged ho- mogeneous ﬁeld at an initial time of 1150 JST, and (c) maximum vertical velocity from 1155 to 1220 JST. These values were determined at each model level within a radius of 5 km from the low-level mesocyclone center. The black arrow in each panel indicates the timing of tornadogenesis.

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FIG. 7. Mixing ratio of hydrometeors (sum of rain, snow, and hail/graupel) at a height of 1 km at (a) 1203, (b) 1206, and (c) 1208 JST. The number of minutes prior to tornadogenesis (i.e., T 2 n min) is shown above the upper-left corner of each panel. The black contours indicate potential temperature of 294 K at a height of 150 m. The contours were smoothed. The black rectangles enclose the area (which is the same in each panel) shown in (d)–(f). Vertical velocity (color scale) at a height of 1 km at (d) 1203, (e) 1206, and (f) 1208 JST. Arrows 2 indicate storm-relative wind vectors, and black contours denote a mixing ratio of hydrometeors of 0.6 g kg 1. Low-MC and low-MA indicate the locations of the low-level mesocyclone and the low-level mesoanticyclone, respectively.

[lowest full level in the model adopting the Lorenz grid; integration is performed around the circuit. The Coriolis Lorenz (1960)]; thus, many vortex lines have their ends term can be neglected because of its small magnitude. near the surface and appear to pierce the ground surface. From Stokes’s theorem, the circulation is equal to the As Markowski et al. (2008) noted, vortex lines do not area integral of vorticity normal to the circuit area; thus, behave as material lines in the presence of vorticity pro- circulation analysis is better suited to target a vortex duction owing to baroclinity and friction; nevertheless, having a certain size than a vorticity budget analysis examination of the conﬁgurations of vortex lines is helpful along a parcel trajectory. Moreover, the calculation er- for understanding the vorticity ﬁeld and storm dynamics. rors can be reduced by distributing the circuit outside the To quantify the contributions of environmental vor- immediate vicinity of a vortex center accompanied by a ticity and storm-generated vorticity to the genesis of large gradient of wind velocity. The material circuit sur- each mesocyclone, the evolution of the circulation for rounding each mesocyclone can be traced backward in each mesocyclone was also analyzed. The circulation time by a backward trajectory analysis using many parcels C(t) can be written as along the circuit. In this study, the circulation analysis was performed by using an approach similar to that of þ Markowski and Richardson (2014). Initially, 1600 parcels 5 Á C(t) v dl, (1) were distributed along the circuit surrounding the tar- geted vortices, and they were integrated backward in time where v is the wind vector and dl represents a displace- adding a parcel on the circuit at a middle point if adjacent ment vector tangent to the circuit. Counterclockwise parcels on the circuit were spaced more than 50 m apart.

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FIG. 8. Evolution of the vorticity ﬁeld until after tornadogenesis. Vertical vorticity (color scale) at a height of 4 km at (a) 1203, (b) 1206, and (c) 1208 JST; at a height of 1 km at (d) 1203, (e) 1206, and (f) 1208 JST; and at a height of 150 m at (g) 1203, (h) 1206, and (i) 1208 JST. Contours (1-hPa interval) denote isobars. Ground-relative wind vectors and gust fronts are shown by arrows and the broken red lines in (g)–(i), respectively. The locations of the midlevel mesocyclone (mid-MC), low-MC, low-MA, and tornado (TR) are indicated. The displayed areas are the same locations as those in Figs. 7d–f. The pink rectangles in (a),(c), and (e) enclose the regions depicted in Figs. 9a, 21a,and13a, respectively.

The backward trajectory of each parcel was calculated by below the lowest model level at z* 5 10 m, as in using a second-order Runge–Kutta scheme with a time Mashiko et al. (2009). step of 0.4 s. Backward trajectory analysis requires fine The time change in circulation can be written as spatiotemporal resolution of the velocity field to re- þ þ duce calculation errors, particularly for a strongly d dp C(t) 52 1 F Á dl, (2) confluent flow such as a tornado (Dahl et al. 2012). In dt r this study, the wind velocities at each parcel location were obtained from the model outputs at 0.8-s intervals where r is density, p is pressure, and F represents the by linear interpolation in time and space. A loga- effect of turbulent mixing and numerical diffusion. The rithmic wind profile assuming a 0.1-m surface rough- variable F includes the near-surface frictional effect, ness was used to extrapolate the near-surface wind which is computed by the surface flux scheme. Here, F

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FIG. 9. (a) Origins of vortex lines (dots) drawn from the midlevel mesocyclone at 4-km height at 1203 JST and vertical vorticity (color scale) in the pink rectangular area shown in Fig. 8a. Note that the color scale of vertical vorticity is different from that of Fig. 8a. Arrows indicate storm-relative winds, and broken contours denote isobars. (b) Horizontal projection of the vortex lines drawn backward from the dots in the midlevel mesocyclone shown in (a). Horizontal vorticity vectors (arrows) at 1500-m height are also shown. (c) Three-dimensional perspective of the vortex lines. The direction of the vortex lines is indicated by the black arrow. below the lowest model level at z* 5 10 m was assumed with those of previous studies using Doppler radar data to have the same value as that at the lowest level. The (Markowski et al. 2012b) and numerical simulation first term on the right-hand side of Eq. (2) represents results (Rotunno and Klemp 1985; Markowski and the baroclinic vorticity generation caused by buoyancy Richardson 2014). torques. b. Vorticity sources of the mesocyclones In this study, each term on the right-hand side of Eq. (2) was calculated directly from the model outputs at 1) MIDLEVEL MESOCYCLONE 0.8-s intervals, unlike in previous studies (Rotunno and Klemp 1985; Mashiko et al. 2009; Markowski et al. Figures 9b and 9c depict the vortex lines passing 2012b; Markowski and Richardson 2014). Addition- through eight points in the midlevel mesocyclone at a ally, the circulation analysis result was verified by height of 4 km, 5 min prior to tornadogenesis (Fig. 9a). comparing the evolution of the circulation calculated Note that the vortex lines are shown only on the side to by integrating the sum of the terms on the right-hand the rear of their origins. All of the vortex lines drawn side of Eq. (2) to that of the circulation calculated di- backward from the midlevel mesocyclone region turn rectly with Eq. (1). Because of the fine spatiotemporal horizontally toward the south-southwest. Most of the resolution of the datasets used in this study, it was vortex lines eventually turn southward at a height of possible to obtain more accurate circulation analysis about 1500 m, but some vortex lines originate in the results for a small vortex such as a tornado, compared southeast at about 500-m height. The directions of

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FIG. 10. (a) The initial position of a material circuit around the midlevel mesocyclone at 4-km height at 1203 JST. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown as in Fig. 9a. (b) Time series of the circulation (solid black line) and the baroclinic (solid red line) and frictional (broken blue line) terms in Eq. (2) for the circuit traced backward in time from 1203 to 1152 JST. The purple dash–dot line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward in time from 1203 JST. The vertical pink lines correspond to the times shown in Fig. 11. thesevortexlinesarenearlycoincidentwiththoseof baroclinity on the circulation was small. As expected, the storm-relative wind and horizontal vorticity asso- the frictional term was nearly zero. This result implies ciated with the environmental vertical wind shear that the midlevel mesocyclone originated from preex- (streamwise vorticity), as shown in the wind hodograph isting environmental vorticity. (Fig. 5a). The configuration of the circuit became more com- The time series of the circulation and its production plicated as it was integrated backward in time terms on the right-hand side of Eq. (2) are shown in (Figs. 11a–d). Although the circuit was not traced into Fig. 10b for a material circuit surrounding the midlevel the far field of the storm (Fig. 11a), the calculated mesocyclone center accompanied by a pressure mini- baroclinic production was close to zero at 1152 JST mum at 4-km height, 5 min prior to tornadogenesis (Fig. 10b). The northern portion of the circuit at the (Fig. 10a). The circuit is traced backward in time to initial time of 1203 JST (Figs. 11d and 12c)descended 1152 JST. Additionally, the integrated circulation, markedly backward in time (Fig. 12b), so that the which was calculated by integrating the baroclinic and northward-directed environmental horizontal vortic- frictional terms in Eq. (2) backward from 1203 JST, is ity vectors were likely to pierce the inside of the circuit compared with the circulation calculated directly with throughout the integration period. These environ- Eq. (1) (cf. the dashed purple and solid black lines in mental vorticity vectors contributed to the positive Fig. 10b). The circulations calculated by these two circulation of the circuit, which indicates that the methods are in good enough agreement during their vorticity source of the midlevel mesocyclone was the evolution to make qualitative inferences except near environmental vertical wind shear with veering. How- the start of the backward time series (around 1202 ever, a horizontal gradient of density was present JST); thus, the calculations of the circulation and each in and around the circuit from 1155 JST (Fig. 12). production term in Eq. (2) are considered reliable. When the baroclinic term was contributing to the It was also confirmed that the results were robust positive circulation at 1159 JST, a southeastward- with respect to the size of the initial material circuit directed horizontal density gradient existed within (not shown). the eastern part of the circuit (Fig. 12a), indicating the The circulation was roughly constant throughout the presence of northeastward-directed baroclinic vor- integration time, although, because of the baroclinic ticity generation there. It is evident from the vertical term, it exhibited a slight up-and-down trend in the projection of the circuit that this baroclinity con- 1155–1203 JST period. However, the net effect of this tributed to the positive circulation of the circuit. In

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FIG. 11. Horizontal projections of the circuit traced backward in time from the midlevel cyclone: (a) 1152, (b) 1159, (c) 1202, and (d) 1203 JST. At the initial time, shown in (d) and Fig. 10a, the circuit surrounds the midlevel mesocyclone. Each circuit was drawn by using 200 parcels and smoothed except for the circuit at the initial time. The color scale indicates circuit heights; gray shading indicates the mixing ratio of hydrometeors at 1-km height; and broken line contours denote potential temperature at 150-m height (2-K interval). The area enclosed by the dashed rectangle in (a) corresponds to the region depicted in (b)–(d).

contrast, at 1202 JST, southward-directed baroclinic contribution to the circulation. It can be inferred that vorticity generation was associated with a westward- this baroclinity was attributable to storm-generated directed density gradient within the circuit (Fig. 12b), positive buoyancy caused by diabatic warming, be- and as a result the baroclinic term made a negative cause the region of low density coincided closely with

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FIG. 12. (a)–(c) Close-ups of the circuits shown in Figs. 11b–d, respectively. The six distinctive symbols indicate corresponding points on the circuit to aid in the visualization of its twisting structure. Black arrows indicate the direction of positive circulation. Gray shading indicates density at heights of (a) 2, (b) 3, and (c) 4 km. the distributions of hydrometeors and high potential To clarify the origin of vertical vorticity in the low- temperature (not shown). level mesocyclone, the time series of the circulation and each production term in Eq. (2) is shown in Fig. 14b for 2) LOW-LEVEL MESOCYCLONE a material circuit encircling the large vertical vorticity Figures 13b and 13c show the vortex lines passing region of the low-level mesocyclone at a height of 1 km, through 10 points in the low-level mesocyclone at 1-km 2 min prior to tornadogenesis (Fig. 14a). These calcula- height, 2 min prior to tornadogenesis (Fig. 13a). After tions are also reliable, as verified by comparing the in- passing through the low-level mesocyclone, some vortex tegrated circulation calculated from production terms lines form arches on its southwest side. The vortex lines on the right-hand side of Eq. (2) with the circulation turn horizontally to the southwest, and then descend to calculated directly with Eq. (1) (Fig. 14b). The results the negative vertical vorticity region in and around the are also robust with respect to the size of the initial anticyclonic vortex a few kilometers southwest of the material circuit (not shown). low-level mesocyclone. These arching vortex lines con- The circulation gradually increased until 1203 JST necting the counter-rotating vortices are similar to those (5 min prior to tornadogenesis); this result differs from the shown in previous studies (Straka et al. 2007; Markowski rapid increase of the circulation of a low-level rotation in et al. 2008, 2012a; Marquis et al. 2012). These studies the 2009 Goshen County storm shown in Markowski suggested that the baroclinically generated horizontal et al. (2012b). This gradual increase was caused mainly vorticity around the RFD associated with the hook echo by the baroclinic term in the 1154–1203 JST period. is the primary vorticity source and is crucial for the de- The frictional term also had a net positive effect on the velopment of the couplet of counter-rotating vortices. gradual increase of the circulation, especially prior to However, the arching vortex lines passing through the 1157 JST, although at certain times it had a negative low-level mesocyclone come from various regions, in- effect. cluding the FFGF and the ground surface beneath the The evolution of the circuit is shown in Fig. 15. The low-level mesocyclone. Moreover, some vortex lines circuit converged on the low-level mesocyclone mainly extend vertically instead of forming arches after pass- from the northeast side near the surface, and most parts ing through the low-level mesocyclone, as shown by of the circuit were present in the inflow sector of Markowski et al. (2008) and Kosiba et al. (2013).Itis the storm at 1200–1206 JST. However, the northwestern very difficult to interpret the configuration of vortex side of the circuit was located along the FFGF, which lines because they are not material lines, owing to was oriented from north-northeast to south-southwest the effects of baroclinity and friction, as noted by and had a 2–3-K horizontal difference of potential Markowski and Richardson (2014). Thus, this result temperature across it. raises the question of whether the baroclinity around the Figure 16 shows the horizontal vorticity vectors at RFD is the dominant vorticity source of the low-level 250-m height around the western portion of the circuit at mesocyclone. 1200 JST, the time at which a gradual increase in

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FIG. 13. (a) Origins of vortex lines (dots) passing through the low-level mesocyclone at 1-km height at 1206 JST and vertical vorticity (color scale) in the pink rectangular area shown in Fig. 8e. Note that the color scale of vertical vorticity is different from that of Fig. 8e. Arrows indicate storm- relative winds, and broken contours denote isobars. The pink rectangle encloses the area shown in Fig. 17a. (b),(c) Three-dimensional distributions of the vortex lines passing through the dots in the low-level mesocyclone in (a) from different viewpoints. The direction of the vortex lines is indicated by black arrows. The horizontal area displayed in (b) and (c) is as that shown in Fig. 8.

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FIG. 14. (a) The initial position of a material circuit around the low-level mesocyclone at 1-km height at 1206 JST. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown as in Fig. 13a. (b) Time series of the circulation (solid black line), baroclinic term (solid red line), and frictional term (dotted blue line) in Eq. (2) for the circuit traced backward in time from 1206 to 1152 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward from 1206 JST. The vertical pink lines correspond to the times shown in Fig. 15. circulation was caused principally by the baroclinic hydrometeor distribution (Fig. 15a). Further investi- term. The large south-southwestward-directed vorticity gation using simulation results with longer model in- vectors generated by baroclinity along the FFGF are tegration and a wider model domain is needed to overlapped by the northwestern portion of the circuit. quantify the contribution of environmental vorticity to The northwestern edge of the circuit is at a higher alti- low-level mesocyclogenesis. tude (above 250 m) around the FFGF, which indicates 3) LOW-LEVEL MESOANTICYCLONE that baroclinity along the FFGF might have contributed to the generation of circulation along the circuit. A similar analysis was conducted for the low-level To quantify the baroclinic contribution around the mesoanticyclone with large negative vertical vorticity at FFGF, the baroclinic term on the right-hand side of Eq. 1-km height, 2 min prior to tornadogenesis. This meso- (2) was evaluated along a small segment (circuit S in anticyclone and the low-level mesocyclone to its north- Fig. 16) of the circuit near the FFGF at 1200 JST. The east constitute a couplet of counter-rotating vortices. 2 baroclinic term value of circuit S was 31.5 m2 s 2, and The configuration of five vortex lines passing through 2 that of the total circuit was 29.8 m2 s 2. These results the mesoanticyclone (Fig. 17a) is quite similar to that of imply that most of the baroclinically generated circula- the low-level mesocyclone vortex lines, including the tion arose along the FFGF, which contributed sub- arches that connect the low-level cyclonic and anticy- stantially to the gradual increase in circulation. clonic vortices (Figs. 17b and 17c). In contrast to the low- At 1158 JST, the entangled circuit was located at level cyclone, however, all of the vortex lines form levels higher than 1000 m on the tip of the hook echo arches. The strong RFD outflow associated with the (Fig. 15b), which was accompanied by large horizontal hook echo is present under these arching vortex lines buoyancy gradients as shown in Part II. However, the (Fig. 7). In contrast to the low-level mesocyclone, the configuration of the circuit at 1158 JST is so complicated vortex lines passing through the mesoanticyclone rise that the effects of baroclinity around the hook remain again and do not extend toward the surface. In fact, the unclear. region of negative vertical vorticity associated with the The circuit for the low-level mesocyclone maintained mesoanticyclone is ambiguous near the surface (Fig. 8h). about two-thirds of its original circulation value for The time series of the circulation and each production 14 min backward in time (Fig. 14b), and the baroclinic term are shown in Fig. 18b for a material circuit sur- production was relatively small at the final integrated rounding the large negative vertical vorticity region of time (1152 JST). However, the circulation was already the mesoanticyclone at a height of 1 km, 2 min prior increasing at 1152 JST, and the circuit stretched to tornadogenesis (Fig. 18a). The integrated and di- across the weak baroclinic zone associated with the rectly calculated circulation values are in approximate

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FIG. 15. Horizontal projections of the circuit traced backward in time from the low-level mesocyclone: (a) 1152, (b) 1158, (c) 1200, and (d) 1206 JST. At the initial time, shown in (d) and Fig. 14a, the circuit surrounds the low-level mesocyclone. The circuit in (a) was drawn by using 1000 parcels, and the circuits in (b)–(d) were drawn by using 200 parcels. The circuits were smoothed, except for that at the initial time shown in (d). The color scale indicates circuit heights; gray shading indicates the mixing ratio of hydrometeors at 1-km height; and broken line contours denote potential temperature at 150-m height (2-K interval). The area enclosed by the black dotted rectangle in (a) corresponds to the regions depicted in (b)–(d). The black dotted rectangle in (c) encloses the area shown in Fig. 16. agreement during their evolution, which indicates that The baroclinic term was dominant around 1158 JST the calculation results are reliable. The results are also and was responsible for the large negative circulation robust with respect to the size of the initial material of the mesoanticyclone. Note that the circulation had circuit, although calculation errors increased as its size a slightly positive value around 1156 JST, which sug- decreased (not shown). gests that the mesoanticyclone originated from the

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FIG. 16. Horizontal vorticity vectors (arrows) and potential temperature (broken contours; 2-K interval) at 250-m height at 1200 JST. Bold solid contours denote the mixing ratio of 2 hydrometeors (0.6 g kg 1 interval; the zero contour is omitted). The displayed area corresponds to the rectangular region in Fig. 15c, and the circuit in Fig. 15c is also shown. The black straight line was used for estimating the baroclinic production of the circulation along a small segment (circuit S) of the circuit (see the text for more details). storm-generated vorticity rather than the environmental shows the horizontal vorticity vectors at 1-km height vorticity associated with vertical wind shear, although around the tip of the hook echo and the intricate circuit further backward integration is needed to evaluate the at 1158 JST. The large horizontal vorticity vectors environmental effect properly. After 1200 JST, the baro- pointing clockwise that surround the tip of the hook clinic term changed its sign to positive and weakened the echo appear to be equivalent to the vortex rings pro- negative circulation (increased the circulation) along with duced by baroclinity around the RFD described in the frictional term. previous studies (Straka et al. 2007; Markowski et al. The evolution of the circuit is shown in Fig. 19. The 2008). It is likely that the baroclinity around the tip of circuit converged on the mesoanticyclone mainly from the hook predominantly produced the negative circu- the southeast side near the surface during the 1202–1206 lation of the mesoanticyclone; however, the circuit was JST period, and the horizontal area encircled by the too convoluted to infer visually from which side the circuit was quite small, in contrast to the area encircled membrane is punctured by the baroclinic-production by the circuit for the low-level mesocyclone. At 1158 vectors. (The buoyancy ﬁeld around the hook echo is JST, at the time of the signiﬁcant enhancement of neg- carefully examined in Part II.) It can be inferred that the ative circulation (rapid decrease in circulation) caused baroclinity around the tip of the hook contributed to principally by the baroclinic term, the northwestern some extent to the generation of the vorticity of the low- portion of the circuit was convoluted at about 1-km level mesocyclone around 1158 JST (see Figs. 14b and height at the tip of the hook echo (Fig. 19a). Figure 20 15b) because some vortex lines passing through the

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FIG. 17. (a) Origins of vortex lines (dots) passing through the low-level mesoanticyclone (the region of large negative vertical vorticity) to the southwest of the low-level mesocyclone at 1-km height at 1206 JST. The displayed area corresponds to the pink rectangular region in Fig. 13a. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown. (b),(c) Three-dimensional distributions of the vortex lines passing through the dots in the low-level mesoanticyclone in (a) from different viewpoints. In (b) the direction of the vortex lines is indicated by black arrows.

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FIG. 18. (a) The initial position of a material circuit around the low-level mesoanticyclone (the region of large negative vertical vorticity) at 1-km height at 1206 JST. Vertical vorticity (color shading), isobars (1-hPa interval), and storm-relative winds (arrows) are also shown as in Fig. 17a. (b) Time series of the circulation (solid black line), baroclinic term (solid red line), and frictional term (dotted blue line) in Eq. (2) for the circuit traced backward in time from 1206 to 1154 JST. The dashed purple line represents the integrated circulation, which was calculated by integrating the sum of the baroclinic and frictional terms backward from 1206 JST. Vertical pink lines correspond to the times shown in Fig. 19. anticyclonic vortex form arches and extend to the low- about 1-km height (Figs. 21e,f), similar to those of the level mesocyclone. midlevel mesocyclone 5 min prior to tornadogenesis (Figs. 9b,c). The vortex lines were directed to the north or north-northeast, which is coincident with the di- 7. Structure changes of the storm before and just rection of the environmental streamwise vorticity as after tornadogenesis shown in the wind hodograph (Fig. 5a). As shown in Fig. 8, the midlevel mesocyclone at 4-km These results suggest that the original midlevel meso- height was located about 3 km ahead (east-northeast cyclone weakened and that the newly generated vortex side) of the low-level mesocyclone until 2 min prior to intensiﬁed on the rear side. As the tornado developed, tornadogenesis. After that, the midlevel mesocyclone this trend became more prominent, and more vortex lines accompanied by a pressure minimum moved slowly (cf. drawn from the midlevel mesocyclone center pass to the 1408E longitude line in Fig. 8) and approached the through the low-level mesocyclone and the tornado (not low-level mesocyclone horizontally (Fig. 8c). That is, the shown). This implies that the low-level vortex intensiﬁed center of the midlevel mesocyclone shifted backward and developed upward. These structure changes of the slightly even in a ground-relative sense just before storm are quite similar to those of the 2009 Goshen tornadogenesis. County storm as described by Markowski et al. (2012a). To clarify the causes of this retrograde motion of the midlevel mesocyclone, vortex line analyses were per- 8. Summary and conclusions formed for two regions of vertical vorticity extrema: one is in the center of the midlevel mesocyclone accompa- On 6 May 2012, an F3 tornado, one of the most de- nied by a pressure minimum and the larger vertical structive tornadoes ever to strike Japan, hit Tsukuba vorticity (Fig. 21a), and the other is on the front side of City and caused severe damage. Radar observations the midlevel mesocyclone (Fig. 21d). Vortex lines drawn revealed that the tornadic storm exhibited typical backward from the midlevel mesocyclone center with characteristics of a ‘‘classic’’ supercell, such as a hook 2 large vertical vorticity of about 0.08 s 1 extend down- echo, a cyclonic rotational wind pattern aloft, a deep ward toward the surface, passing in the vicinity of structure with echo top exceeding a height of 10 km, the low-level mesocyclone (Figs. 21b,c). Meanwhile, the and a strong tornado at the tip of the hook echo. Triply vortex lines drawn backward from the front side of the nested high-resolution simulations were conducted us- midlevel mesocyclone center turn horizontally toward ing the Japan Meteorological Agency Nonhydrostatic the south and originate in the storm environment at Model (JMANHM). The innermost 50-mesh simulation

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FIG. 19. Horizontal projections of the circuit traced backward in time from the low-level mesoanticyclone: (a) 1158, (b) 1202, and (c) 1206 JST. At the initial time, shown in (c) and Fig. 18a, the circuit surrounds the region of large negative vertical vorticity. Each circuit was drawn using 200 parcels and smoothed, except for that at the initial time shown in (c). The color scale indicates circuit heights; gray shading indicates the mixing ratio of hydrometeors at 1-km height; and broken contours denote potential temperature at 150-m height (2-K interval). successfully reproduced the typical ‘‘classic’’ supercell the storm led to an up-and-down trend of the circulation. storm as well as the tornado, as in the radar observa- The net effect of this baroclinity on the circulation was tions. This simulation adopted a realistic experimental relatively small. design that included surface friction and used initial In contrast, some vortex lines passing through the low- and boundary conditions obtained by the four- level mesocyclone 2 min prior to tornadogenesis formed dimensional variational data assimilation technique of the JMA. The simulated storm exhibited the features of a typical tornadic supercell. In the early stage, a broad mesocyclone at midlevel was present about 3 km horizontally ahead of the low-level circulation center before tornadogenesis. The low-level mesocyclone intensi- ﬁed with time at around 1-km height, and the updraft associated with the low-level mesocyclone exceeded 2 20 m s 1 at 500-m height, 2 min prior to tornadogenesis. A low-level mesoanticyclone also developed to the southwest of the low-level mesocyclone. The tornado was subsequently generated on the RFGF at the tip of the hook echo, which was nearly directly beneath the low-level mesocyclone. Analyses of vortex lines and circulation were performed to clarify the vorticity sources of the midlevel mesocyclone, low-level mesocyclone, and low-level mesoanticyclone. All of the vortex lines that passed through the midlevel mesocyclone originated from the environmental streamwise vorticity, where a strong vertical wind shear FIG. 20. Horizontal vorticity vectors (arrows) at 1-km height at 2 22 1158 JST. The bold solid contours denote the mixing ratio of hy- existed and the 0–3-km SREH value was 556 m s .In 2 drometeors; the contour interval is 0.6 g kg 1, but the zero contour fact, most of the circulation of the material circuit sur- is omitted. The area shown corresponds to that enclosed by the rounding the midlevel mesocyclone was retained, al- black dotted rectangle in Fig. 19a, and the circuit is also shown, as in though the baroclinity due to diabatic warming within Fig. 19a.

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FIG. 21. (a) Origins of vortex lines (dots) drawn from the midlevel mesocyclone at 4-km height at 1208 JST (just after tornadogenesis) and vertical vorticity (color scale) in the area enclosed by the pink rectangle in Fig. 8c. Note that the color scale of vertical vorticity is different from that of Fig. 8c. Arrows indicate storm-relative winds, and broken contours denote isobars. (b) Horizontal projection of the vortex lines drawn backward from the dots on the midlevel mesocyclone in (a). (c) As in (b), but from a three-dimensional perspective. In (b) and (c), the direction of the vortex lines is indicated by the black arrows, and the horizontal area is the same as that shown in Fig. 8. (d)– (f) As in (a)–(c), but the origins of vortex lines are displaced to the front side of the midlevel mesocyclone. arches and extended to the low-level anticyclonic vor- All of the vortex lines that passed through the low- tex, as shown in previous studies (Straka et al. 2007; level mesoanticyclone with a large negative vertical Markowski et al. 2008, 2012a). However, the circulation vorticity 2 min prior to tornadogenesis formed arches. of a circuit encircling the low-level mesocyclone grad- Most of the negative circulation about the material cir- ually increased, mainly owing to the baroclinity along cuit surrounding the mesoanticyclone was acquired the FFGF. The surface friction also had a positive net rapidly owing to baroclinity around the tip of the hook effect on the circulation. This result differs from that of a echo. This suggests that the mesoanticyclone did not low-level mesocyclone shown by Markowski et al. originate from the preexisting environmental vorticity (2012b) and the tornado described in Part II, which but from the storm-generated vorticity. However, fur- showed the rapid increase of circulation caused by ther backward trace of the circuit will be needed to baroclinity. evaluate the environmental effect properly.

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The vortex line analysis also revealed that just after Storms, Kananaskis Park, AB, Canada, Amer. Meteor. Soc., tornadogenesis, the low-level mesocyclone intensified 588–592. significantly and developed upward, which caused ret- ——, R. J. Trapp, and H. B. Bluestein, 2001: Tornadoes and tornadic storms. Severe Convective Storms, Meteor. Monogr.,No rograde motion of the midlevel mesocyclone. 50, Amer. Geophys. Union, 175–180. Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derived Acknowledgments. The author acknowledges helpful from a three-dimensional model. Bound.-Layer Meteor., 18, comments by Hiroshi Niino, Teruyuki Kato, and Hiroshi 495–527, doi:10.1007/BF00119502. Yamauchi. The author also extends thanks to Yvette Ikawa, M., H. Mizuno, T. Matsuo, M. Murakami, Y. Yamada, and K. 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